What is the integral from 0 to 10 of 25-(t-5)^2 ?

The integral from 0 to 10 of 25-(t-5)^2 is 500/3

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integral from 0 to 10 of 25-(t-5)^2

\int_{0}^{10} 25 - (t - 5)^{2} d t

\frac{500}{3}

Decimal

166.66666 \dots

Solution steps

\int_{0}^{10} 25 - (t - 5)^{2} d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{10} 25 d t - \int_{0}^{10} (t - 5)^{2} d t

\int_{0}^{10} 25 d t = 250

\int_{0}^{10} (t - 5)^{2} d t = \frac{250}{3}

= 250 - \frac{250}{3}

Simplify

250 - \frac{250}{3} : \frac{500}{3}

= \frac{500}{3}

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What is the integral from 0 to 10 of 25-(t-5)^2 ?
The integral from 0 to 10 of 25-(t-5)^2 is 500/3